Waves

The equation of a transverse wave travelling along a string is y = 0.05 sin(4πx − 200πt) m, where x is in metres and t in seconds. What is the speed of the wave?

For the wave y = 0.05 sin(4πx − 200πt) m described above, what is the maximum speed of a particle of the string?

A stretched wire under tension T supports a transverse wave of speed V. If the tension is increased to 4T while the mass per unit length stays the same, what is the new wave speed?

Two wires of the same material, under the same tension, have diameters in the ratio 1 : 2 (thin : thick). What is the ratio of wave speeds on them (thin wire : thick wire)?

Calculate the speed of sound in a gas with pressure 1.0 × 10⁵ Pa, density 1.3 kg/m³, and γ = 1.4.

The speed of sound in air at 0°C is 332 m/s. Using V_t = V₀ + 0.61t, find the speed of sound at 30°C.

Two coherent sound waves of amplitude ratio 3 : 2 superpose at a point. What is the ratio I_max : I_min at that point?

A tuning fork of frequency 256 Hz produces 4 beats per second with an unknown tuning fork. When the unknown fork is loaded with a little wax (which lowers its frequency), the beat frequency decreases to 2 beats per second. What is the frequency of the unknown fork?

A closed organ pipe is 25 cm long. Taking the speed of sound in air as 340 m/s and ignoring end correction, find its fundamental frequency.

An open organ pipe of length 1 m resonates at 510 Hz, which is one of its overtones. Taking the speed of sound as 340 m/s, which harmonic is this?

In a resonance tube experiment using a tuning fork of frequency 512 Hz, the first and second resonance lengths are found to be 16.5 cm and 50.5 cm. Calculate the speed of sound in air.

In a resonance tube, the first resonance length is 17 cm and the second is 53 cm. Find the end correction (e).

A sonometer wire of length L under tension T vibrates at its fundamental frequency n. If the tension is increased to 2.25T (length unchanged), what is the new fundamental frequency?

A wire vibrating in its fundamental mode at frequency n is replaced by an identical wire of double the length, under the same tension and with the same mass per unit length. In how many loops (segments) must the new wire vibrate to produce the same frequency n?

A train sounds its whistle of frequency 480 Hz while approaching a stationary observer at 30 m/s. Taking the speed of sound as 330 m/s, what frequency does the observer hear?

A stationary source emits sound of frequency 600 Hz. An observer moves directly away from the source at 20 m/s. Taking the speed of sound as 340 m/s, what frequency does the observer hear?

A source of frequency 500 Hz moves towards a stationary listener at 20 m/s, while the listener simultaneously moves towards the source at 10 m/s. Taking the speed of sound as 340 m/s, find the apparent frequency heard.

A jet flies at a speed of 680 m/s through air where the speed of sound is 340 m/s. What is the half-angle of the conical shock wave it produces?