Waves

In an experiment to determine the velocity of sound in air at room temperature using a resonance tube, the first resonance is observed when the air column has a length of 20.0 cm for a tuning fork of frequency 400 Hz is used. The velocity o...

The velocity of sound in a gas, in which two wavelengths 4.08 m and 4.16 m produce 40 beats in 12s, will be :

A tunning fork of frequency 340 Hz resonates in the fundamental mode with an air column of length 125 cm in a cylindrical tube closed at one end. When water is slowly poured in it, the minimum height of water required for observing resonanc...

The frequency of echo will be __________ Hz if the train blowing a whistle of frequency 320 Hz is moving with a velocity of 36 km/h towards a hill from which an echo is heard by the train driver. Velocity of sound in air is 330 m/s.

In the wave equation
\(y=0.5 \sin \frac{2 \pi}{\lambda}(400 \mathrm{t}-x) \,\mathrm{m}\)
the velocity of the wave will be:

An observer moves towards a stationary source of sound with a velocity equal to one-fifth of the velocity of sound. The percentage change in the frequency will be :

If a wave gets refracted into a denser medium, then which of the following is true?

A wire of length 30 cm, stretched between rigid supports, has it's nth and (n + 1)th harmonics at 400 Hz and 450 Hz, respectively. If tension in the string is 2700 N, it's linear mass density is ____________ kg/m.

A set of 20 tuning forks is arranged in a series of increasing frequencies. If each fork gives 4 beats with respect to the preceding fork and the frequency of the last fork is twice the frequency of the first, then the frequency of last for...

When a car is approaching the observer, the frequency of horn is \(100 \mathrm{~Hz}\). After passing the observer, it is \(50 \mathrm{~Hz}\). If the observer moves with the car, the frequency will be \(\frac{x}{3} \mathrm{~Hz}\) where $$x=$...

A transverse wave is represented by \(y=2 \sin (\omega t-k x)\, \mathrm{cm}\). The value of wavelength (in \(\mathrm{cm}\)) for which the wave velocity becomes equal to the maximum particle velocity, will be :

The first overtone frequency of an open organ pipe is equal to the fundamental frequency of a closed organ pipe. If the length of the closed organ pipe is 20 cm. The length of the open organ pipe is _____________ cm.

An observer is riding on a bicycle and moving towards a hill at \(18 \,\mathrm{kmh}^{-1}\). He hears a sound from a source at some distance behind him directly as well as after its reflection from the hill. If the original frequency of the ...

Two waves executing simple harmonic motions travelling in the same direction with same amplitude and frequency are superimposed. The resultant amplitude is equal to the \(\sqrt3\) times of amplitude of individual motions. The phase differen...

The equations of two waves are given by :
y1 = 5 sin 2\(\pi\)(x - vt) cm
y2 = 3 sin 2\(\pi\)(x \(-\) vt + 1.5) cm
These waves are simultaneously passing through a string. The amplitude of the resulting wave is :

Two travelling waves of equal amplitudes and equal frequencies move in opposite directions along a string. They interfere to produce a stationary wave whose equation is given by \(y = (10\cos \pi x\sin {{2\pi t} \over T})\) cm
The amplitude...

A wire having a linear mass density 9.0 \(\times\) 10\(-\)4 kg/m is stretched between two rigid supports with a tension of 900 N. The wire resonates at a frequency of 500 Hz. The next higher frequency at which the same wire resonates is 550...

Two cars X and Y are approaching each other with velocities 36 km/h and 72 km/h respectively. The frequency of a whistle sound as emitted by a passenger in car X, heard by the passenger in car Y is 1320 Hz. If the velocity of sound in air i...

A tuning fork is vibrating at 250 Hz. The length of the shortest closed organ pipe that will resonate with the tuning fork will be __________ cm. (Take speed of sound in air as 340 ms\(-\)1)

The mass per unit length of a uniform wire is 0.135 g/cm. A transverse wave of the form y = \(-\) 0.21 sin (x + 30t) is produced in it, where x is in meter and t is in second. Then, the expected value of tension in the wire is x \(\times\) ...

A tuning fork A of unknown frequency produces 5 beats/s with a fork of known frequency 340 Hz. When fork A is filed, the beat frequency decreases to 2 beats/s. What is the frequency of fork A?

Two travelling waves produces a standing wave represented by equation,y = 1.0 mm cos(1.57 cm\(-\)1) x sin(78.5 s\(-\)1)t. The node closest to the origin in the region x > 0 will be at x = .............. cm.

A source and a detector move away from each other in absence of wind with a speed of 20 m/s with respect to the ground. If the detector detects a frequency of 1800 Hz of the sound coming from the source, then the original frequency of sourc...

Two waves are simultaneously passing through a string and their equations are : y1 = A1 sin k(x \(-\) vt), y2 = A2 sin k(x \(-\) vt + x0). Given amplitudes A1 = 12 mm and A2 = 5 mm, x0 = 3.5 cm and wave number k = 6.28 cm\(-\)1. The amplitu...

A student is performing the experiment of resonance column. The diameter of the column tube is 6 cm. The frequency of the tuning fork is 504 Hz. Speed of the sound at the given temperature is 336 m/s. The zero of the metre scale coincides w...

The percentage increase in the speed of transverse waves produced in a stretched string if the tension is increased by 4%, will be __________%.

Two cars are approaching each other at an equal speed of 7.2 km/hr. When they see each other, both blow horns having frequency of 676 Hz. The beat frequency heard by each driver will be ___________ Hz. [Velocity of sound in air is 340 m/s.]

Which of the following equations represents a travelling wave?

The motion of a mass on a spring, with spring constant K is as shown in figure.The equation of motion is given by x(t) = A sin\(\omega\)t + B cos\(\omega\)t with \(\omega\) = \(\sqrt {{K \over m}}\)Suppose that at time t = 0, the position ...

The amplitude of wave disturbance propagating in the positive x-direction is given by \(y = {1 \over {{{(1 + x)}^2}}}\) at time t = 0 and \(y = {1 \over {1 + {{(x - 2)}^2}}}\) at t = 1 s, where x and y are in metres. The shape of wave does ...

The frequency of a car horn encountered a change from 400 Hz to 500 Hz, when the car approaches a vertical wall. If the speed of sound is 330 m/s. Then the speed of car is ___________ km/h.

A sound wave of frequency 245 Hz travels with the speed of 300 ms\(-\)1 along the positive x-axis. Each point of the wave moves to and from through a total distance of 6 cm. What will be the mathematical expression of this travelling wave?

A closed organ pipe of length L and an open organ pipe contain gases of densities \(\rho\)1 and \(\rho\)2 respectively. The compressibility of gases are equal in both the pipes. Both the pipes are vibrating in their first overtone with same...

Three harmonic waves having equal frequency
\(\nu\) and same intensity \({I_0}\), have phase angles 0, \({\pi \over 4}\) and \(- {\pi \over 4}\) respectively. When they are
superimposed the intensity of the resultant wave
is close to :

A wire of length L and mass per unit length
6.0 × 10–3 kgm–1 is put under tension of
540 N. Two consecutive frequencies that it
resonates at are : 420 Hz and 490 Hz. Then L
in meters is :

A one metre long (both ends open) organ pipe
is kept in a gas that has double the density of
air at STP. Assuming the speed of sound in air
at STP is 300 m/s, the frequency difference
between the fundamental and second harmonic
of this pipe...

A transverse wave travels on a taut steel wire
with a velocity of v when tension in it is
2.06 × 104 N. When the tension is changed to
T, the velocity changed to v/2. The value of T
is close to :

Speed of a transverse wave on a straight wire (mass 6.0 g, length 60 cm and area of cross-section 1.0 mm2) is 90 ms-1. If the Young's modulus of wire is 16 \(\times\) 1011 Nm-2, the extension of wire over its natural length is :

A stationary observer receives sound from two identical tuning forks, one of which approaches
and the other one recedes with the same speed (much less than the speed of sound). The
observer hears 2 beats/sec. The oscillation frequency of ea...

A sound source S is moving along a straight track with speed v, and is emitting, sound of frequency
v0
(see figure). An observer is standing at a finite distance, at the point O, from the track. The
time variation of frequency heard by the...

In a resonance tube experiment when the tube
is filled with water up to a height of 17.0 cm
from bottom, it resonates with a given tuning
fork. When the water level is raised the next
resonance with the same tuning fork occurs at
a height o...

Assume that the displacement(s) of air is
proportional to the pressure difference (\(\Delta\)p)
created by a sound wave. Displacement (s)
further depends on the speed of sound (v),
density of air (\(\rho\)) and the frequency (f). If
$$\De...

A driver in a car, approaching a vertical wall
notices that the frequency of his car horn, has
changed from 440 Hz to 480 Hz, when it gets
reflected from the wall. If the speed of sound in
air is 345 m/s, then the speed of the car is :

For a transverse wave travelling along a straight line, the distance between two peaks (crests) is 5 m, while the distance between one crest and one trough is 1.5 m. The possible wavelengths (in m) of the are :

The driver of a bus approaching a big wall notices that the frequency of his bus's horn changes
from 420 Hz to 490 Hz when he hears it after it gets reflected from the wall. Find the speed of the
bus if speed of the sound is 330 ms–1.

A uniform thin rope of length 12 m and mass 6 kg hangs vertically from a rigid support and a block
of mass 2 kg is attached to its free end. A transverse short wavetrain of wavelength 6 cm is
produced at the lower end of the rope. What is t...

Two identical strings X and Z made of same
material have tension TX and TZ in them. If their
fundamental frequencies are 450 Hz and
300 Hz, respectively, then the ratio TX/TZ is

A heavy ball of mass M is suspendeed from the ceiling of a car by a light string of mass m (m < < M). When the car is at rest, the speed of transverse waves in the string is 60 ms\(-\)1. When the car has acceleration a, the wave-speed incre...

A musician using an open flute of length 50 cm producess second harmonic sound waves. A person runs towards the musician from another end of hall at a speed of 10 km/h. If the wave speed is 330 m/s, the frequency heard by the running perso...

The pressure wave, P = 0.01 sin [1000t – 3x] Nm–2,
corresponds to the sound produced by a vibrating blade
on a day when atmospheric temperature is 0°C. On
some other day, when temperature is T, the speed of
sound produced by the same blade ...