Standing Waves

A sound wave is transmitted into a tube as shown in the figure. The sound wave splits into two waves at point A which recombine at point B. Let R be the radius of the semi-circle which is varied until the first minimum. Calculate the radius of the semi-circle if the wavelength of the sound is 50.0 m.

Police in a siren car moving with a velocity 20 ms^– chases a thief who is moving in a car with a velocity v₀ ms^-1. The police car sounds at frequency 300 Hz, and both of them move towards a stationary siren of frequency 400 Hz. Calculate the speed in which thief is moving. (Assume the thief does not observe any beat)

For a particular tube, among six harmonic frequencies below 1000 Hz, only four harmonic frequencies are given: 300 Hz, 600 Hz, 750 Hz and 900 Hz. What are the two other frequencies missing from this list?

Let y = `1/(1 + x^2)` at  t = 0 be the amplitude of the wave propagating in the positive x-direction. At t = 2s, the amplitude of the wave propagating becomes y = `1/(1 + (x - 2)^2)`. Assume that the shape of the wave does not
change during propagation. The velocity of the wave is:

What is a stationary wave?

Explain the formation of stationary waves.

Write the characteristics of stationary waves.

Discuss the law of transverse vibrations in stretched strings.