A transverse harmonic wave on a string is given by

$$y(x,t) = 5\sin (6t + 0.003x)$$

where x and y are in cm and t in sec. The wave velocity is _______________ ms$$^{-1}$$.

A guitar string of length 90 cm vibrates with a fundamental frequency of 120 Hz. The length of the string producing a fundamental frequency of 180 Hz will be _________ cm.

An organ pipe $$40 \mathrm{~cm}$$ long is open at both ends. The speed of sound in air is $$360 \mathrm{~ms}^{-1}$$. The frequency of the second harmonic is ___________ $$\mathrm{Hz}$$.

A person driving car at a constant speed of $$15 \mathrm{~m} / \mathrm{s}$$ is approaching a vertical wall. The person notices a change of $$40 \mathrm{~Hz}$$ in the frequency of his car's horn upon reflection from the wall. The frequency of horn is _______________ $$\mathrm{Hz}$$.

(Given: Speed of sound : $$330 \mathrm{~m} / \mathrm{s}$$ )