Waves

For sound waves, if the number of nodes for the $5^{\text {th }}$ harmonic of an open-ended pipe is $n$ and that for the $9^{\text {th }}$ harmonic of the same pipe with one of its ends closed is $m$, the ratio $\frac{n}{m}$ is

For a travelling harmonic wave
$y(x, t)=2.0 \cos 2 \pi(10 t-0.0080 x+0.35)$, where $x$ and $y$ are in cm and $t$ in $s$. The phase difference between oscillatory motion of two points separated by a distance of 0.5 m is:

 A pipe open at both ends has a fundamental frequency $f$ in air. The pipe is now dipped vertically in a water drum to half of its length. The fundamental frequency of the air column is now equal to:

The displacement of a travelling wave \(y=C \sin \frac{2 \pi}{\lambda}\) (at \(-x\)) where \(t\) is time, \(x\) is distance and \(\lambda\) is the wavelength, all in S.I. units. Then the frequency of the wave is

The \(4^{\text {th }}\) overtone of a closed organ pipe is same as that of \(3^{\text {rd }}\) overtone of an open pipe. The ratio of the length of the closed pipe to the length of the open pipe is :

The ratio of frequencies of fundamental harmonic produced by an open pipe to that of closed pipe having the same length is

An organ pipe filled with a gas at 27\(^\circ\)C resonates at 400 Hz in its fundamental mode. If it is filled with the same gas at 90\(^\circ\)C, the resonance frequency at the same mode will be

If the initial tension on a stretched string is doubled, then the ratio of the initial and final speeds of a transverse wave along the string is

In a guitar, two strings A and B made of same material are slightly out of tune and produce beats of frequency 6 Hz. When tension in B is slightly decreased, the beat frequency of A is 530 Hz, the original freqnency of B will be :

A tuning fork is used to produce resonance in
a glass tube. The length of the air column in
this tube can be adjusted by a variable piston.
At room temperature of 27°C two successive
resonances are produced at 20 cm and 73 cm
of column leng...

The fundamental frequency in an open organ
pipe is equal to the third harmonic of a closed
organ pipe. If the length of the closed organ
pipe is 20 cm, the length of the open organ
pipe is

Two cars moving in opposite directions approach each other with speed of 22 m s\(-\)1 and 16.5 m s\(-\)1 respectively. The driver of the first car blows a horn having a frequency 400 Hz. The frequency heard by the driver of the second car i...

The two nearest harmonics of a tube closed at one end and open at other end are 220 Hz and 260 Hz. What is the fundamental frequency of the system ?

The second overtone of an open organ pipe has the same frquency as the first overtone of a closed pipe L metre long. The length of the open pipe will be

Three sound waves of equal amplitudes have frequencies (n \(-\) 1), n, (n + 1). They superimpose to give beats. The number of beats produced per second will be

A siren emitting a sound of frequency 800 Hz moves away from an observer towards a cliff at a speed of 15 m s\(-\)1. Then, the frequency of sound that the observer hears in the echo reflected from the cliff is
(Take velocity of sound in ai...

A uniform rope of length L and mass m1 hangs vertically from a rigid support. A block of mass m2 is attached to the free end of the rope. A transverse pulse of wavelength \(\lambda\)1 is produced at the lower end of the rope. The wavelen...

An air column, closed at one end open at the other, resonates with a tuning fork when the smallest length of the column is 50 cm. The next larger length of the column resonating with the same tuning fork is

The fundamental frequency of a closed organ pipe of length 20 cm is equal to the second overtone of an organ pipe open at both the ends. The length of organ pipe open at both the ends is

4.0 g of a gas occupies 22.4 litres at NTP. The specific heat capacity of the gas at constant volume is 5.0 J K\(-\)1 mol\(-\)1. If the speed of sound in this gas at NTP is 952 m s\(-\)1, then the heat capacity at constant pressure is
(Ta...

A string is stretched between fixed points separated by 75.0 cm. It is observed to have resonant frequencies of 420 Hz and 315 Hz. There are no other resonant frequencies between these two. The lowest resonant frequency for this string i...

A source of sound S emitting waves of frequency 100 Hz and an observer O are located at some distance from each other. The source is moving with a speed of 19.4 m s\(-\)1 at an angle of 60o with the source observer line as shown in the figu...

The number of possible natural oscillations of air column in a pipe closed at one end length 85 cm whose frequencies lie below 1250 Hz are (Velocity of sound = 340 m s\(-\)1)

A speeding motorcyclist sees traffic jam ahead him. He slows down to 36 km hour\(-\)1. He finds that traffic has eased and a car moving ahead of him at 18 km hour\(-\)1 is honking at a frequency of 1392 Hz. If the speed of sound is 343 m s...

If n1, n2 and n3 are the fundamental frequencies of three segments into which a string is divided, then the original fundamental frequency n of the string is given by

Two sources P and Q produce notes of frequency 660 Hz. each. A listener moves from P to Q with a speed of 1 ms\(-\)1. If the speed of sound is 330 m/s, then the number of beats heard by the listener per second will be

The length of the wire between two ends of a sonometer is 100 cm. What should be the positions of two bridges below the wire so that the three segments of the wire have their fundamental frequencies in the ratio 1 : 3 : 5.

If we study the vibration of a pipe open at both ends. then the following statement is not true.

A source of unknown frequency gives 4 beats/s when sounded with a source of known frquency 250 Hz. The second harmonic of the source of unknown frequency gives five beats per second, when sounded with a source of frequency 513 Hz. The unkno...

A wave travelling in the + ve x-direction having displacement along y-direction as 1 m, wavelength 2\(\pi\) m and frequency of \({1 \over \pi }\) Hz is represented by

Two sources of sound placed close to each other, are emitting progressive waves given by
y1 = 4sin600\(\pi\)t and y2 = 5sin608\(\pi\)t
An observer located near these two sources of sound will hear

When a string is divided into three segments of length \(l\)1, \(l\)2 and \(l\)3 the fundamental frequencies of these three segments are \({\upsilon _1},{\upsilon _2}\) and \({\upsilon _3}\) respectively. The original fundamental frequency ...

The equation of a simple harmonic wave is given by
y = 3 sin\({\pi \over 2}\)(50t \(-\) x),
where x and y are in metres and t is in seconds. The ratio of maximum particle velocity to the wave velocity is

A train moving at a speed of 220 m s\(-\)1 towards a stationary object, emits a sound of frequency 1000 Hz. Some of the sound reaching the object gets reflected back to the train as echo. The frequency of the echo as detected by the driver ...

Two waves are represented by the equations
y1 = \(a\)sin(\(\omega\)t + kx + 0.57) m and
y2 = acos(\(\omega\)t + kx) m, where x is in meter and t \(in\) sec. The phase difference between them is

Sound waves travel at 350 m/s through a warm air and at 3500 m/s through brass. The wavelength of a 700 Hz acoustic wave as it enters brass from warm air

Two identical piano wires, kept under the same tension T have a fundamental frequency of 600 Hz. The fractional increase in the tension of one of the wires which will lead to occurrence of 6 beats/s when both the wires oscillate together wo...

A tuning fork of frequency 512 Hz makes 4 beats per second with the vibrating string of a piano. The beat frequency decreases to 2 beats per sec when the tension in the piano string is slightly increased. The frequency of the piano string ...

A transverse wave is represented by
y = Asin(\(\omega\)t \(-\) kx). For what value of the wavelength is the wave velocity equal to the maximum particle velocity ?

A wave in a string has an amplitude of 2 cm. The wave travels in the +ve direction of x axis with a speed of 128 m/s. and it is noted that 5 complete waves fit in 4m length of the string. The equation describing the wave is

Each of the two strings of length 51.6 cm and 49.1 cm are tensioned separately by 20 N force. Mass per unit length of both the strings is same and equal to 1 g/m. When both the strings vibrate simultaneously the number of beats is

The driver of a car travelling with speed 30 m/s towards a hill sounds a horn of frequency 600 Hz. If the velocity of sound in air is 330 m/s, the frequency of reflected sound as heard by driver is

Two periodic waves of intensities \(I\)1 and \(I\)2 pass through a region at the same time in the same direction. The sum of the maximum and minimum intensities is

A point performs simple harmonic oscillation of period T and the equation of motion is given by x = a sin(\(\omega\)t + \(\pi\)/6). After the elapse of what fraction of the time period the velocity of the point will be equal to half of it...

The wave described by y = 0.25 sin(10\(\pi\)x \(-\) 2\(\pi\)t), where x and y are in metres and t in seconds, is a wave travelling along the

Which one of the following statements is true ?

A transverse wave propagating along x-axis is represented by y(x, t) = 8.0 sin (0.5 \(\pi\)x \(-\) 4\(\pi\)t \(-\) \(\pi\)/4) where x is in metres and t is in seconds. The speed of the wave is

The time of reverberation of a room A is one second. What will be the time (in seconds of reverberation of a room, having all the dimensions double of those of room A ?

Two vibrating tuning forks produce waves given by y1 = 4 sin 500\(\pi\)t and y2 = 2 sin506 \(\pi\)t. Number of beats produced per minute is

Two sound waves with wavelengths 5.0 m and 5.5. m respectively, each propagate in a gas with velocity 330 m/s. We expect the following number of beats per second.