Waves - Mechanics - Physics Previous Year Questions

The equation of a progressive wave can be given by \(y=15\sin(660\pi t-0.02\pi x)\) cm. The frequency of the wave is

A source of sound gives 5 beats per second, when sounded with another source of frequency 100 s\(^{-1}\). The second harmonic of the source, together with a source of frequency 205 s\(^{-1}\) gives 5 beats per second. What is frequency of the source?

The displacement of a wave is given by

$$y = 20\cos (\omega t + 4z)$$

The amplitude of the given wave is

If frequencies are \((\nu-1)\) and \((\nu+2)\), then find the value of beats.

The string of length 2 m is fixed at both ends. If the string vibrates in its fourth normal mode with a frequency of 500 Hz, then the waves would travel on it with a velocity of

A source of sound emits sound waves at frequency \(f_0\). It is moving towards an observer with fixed speed \({v_s}\) (\({v_s},v\), where \(v\) is the speed of sound in air.) If the observers were to move towards the source with speed \(v_0\), one of the following two graphs (A and B) will give the correct variation of the frequency \(f\) heard by the observer as \(v_0\) is changed.

The variation of \(f\) with \(v_0\) is given correctly by

A bat emitting an ultrasonic wave of frequency 4.5 \(\times\) 10⁴ Hz at speed of 6 m/s between two parallel walls. The two frequencies heard by the bat will be

Two open organ pipes A and B of length \(22 \mathrm{~cm}\) and \(22.5 \mathrm{~cm}\) respectively produce 2 beats per sec when sounded together. The frequency of the shorter pipe is

A tuning fork of unknown frequency produces 4 beats with tuning fork of frequency \(310 \mathrm{~Hz}\). It gives the same number of beats on filing. The initial frequency of a tuning fork is

The number of possible natural oscillations of air column in a pipe closed at one end of length \(85 \mathrm{~cm}\) whose frequencies lie below \(1250 \mathrm{~Hz}\) are (velocity of sound \(=340 \mathrm{~ms}^{-1}\))

A string of length \(25 \mathrm{~cm}\) and mass \(10^{-3} \mathrm{~kg}\) is clamped at its ends. The tension in the string is \(2.5 \mathrm{~N}\). The identical wave pulses are generated at one end and at regular interval of time, \(\Delta \mathrm{t}\). The minimum value of \(\Delta \mathrm{t}\), so that a constructive interference takes place between successive pulses is

A car is moving towards a high cliff. The car driver sounds a horn of frequency \(f\). The reflected sound heard by the driver has a frequency \(2 f\). If \(v\) be the velocity of sound, then the velocity of the car in the same velocity units, will be

With what velocity should an observer approach a stationary sound source, so that the apparent frequency of sound should appear double the actual frequency?

A string vibrates with a frequency of \(200 \mathrm{~Hz}\). When its length is doubled and tension is altered, it begins to vibrate with a frequency of \(300 \mathrm{~Hz}\). The ratio of the new tension to the original tension is

The speed of transverse wave in aluminium wire is $\frac{1}{10}$ times the speed of longitudinal wave in the wire. The stress in the wire is (Young's Modulus of Al=10 ${ }^{10} \mathrm{~Pa}$ )

Resonance is produced between a turning fork and a resonance column tube with upper end open and lower end closed by water surface. If the frequency of the tuning fork is 800 Hz , and first two resonances are observed at lengths $9.75 \mathrm{~cm}, 31.25 \mathrm{~cm}$,

Find the length at which the third resonance occurs? Also find the speed of sound.