Mechanics Waves Mock Tests

A sound source of frequency f_s = 1000 Hz moves toward a wall with speed v_s = v/5, where v is the speed of sound. An observer moves toward the wall with speed v_o = v/5 directly behind the source. The observer hears both the direct sound from the source and the sound reflected from the wall. Find the beat frequency heard by the observer.

A string of length L is fixed at both ends with uniform linear mass density μ and tension T. The fundamental frequency of transverse vibration is:

A composite string is formed by joining two strings of linear mass densities μ and 4μ at one end. The composite string is under tension T and has total length 3L, with each segment of length L. The free end of the lighter string is fixed, and the free end of the heavier string is also fixed. Find the lowest normal mode frequency f of this system, given that there is a node at the junction.

Two strings of different linear mass densities μ₁ and μ₂ are joined together at one end. The combined string is stretched with uniform tension T and both ends are fixed. The lengths of the two segments are L₁ and L₂ respectively. If the junction point is a node, the possible angular frequencies of normal mode vibration are:

A sound source moves toward a stationary observer at speed v_s = v/3 where v is the speed of sound. The observer then moves away from the source (which is now stationary) at speed v_o = v/3. The ratio of the apparent frequencies f₁/f₂ is:

A sound source of frequency f_0 moves towards a stationary observer with speed v_s. The observer also moves towards the source with speed v_o. If v_s = v_o = v/3 where v is the speed of sound, the apparent frequency heard by the observer is:

A string of length L is fixed at both ends and has uniform linear mass density mu. The tension in the string is T = T_0*(1 + x/L) where x is the distance from one end. The fundamental frequency of vibration is approximately: