A closed organ pipe is sounded near a guitar, causing one of the strings to vibrate with large amplitude. We vary the tension of the string until we find the maximum amplitude. The string is $80\%$ as long as the closed pipe. If both the pipe and the string vibrate at their fundamental frequency, calculate the ratio of the wave speed on the string to the speed of sound in air.

Two identical violin strings, when in tune and stretched with the same tension have a fundamental frequency of $440.0 \mathrm{Hz}$. One of the strings is retuned by adjusting its tension. When this is done, $1.5$ beats per second are heard when both strings are plucked simultaneously. (a) What are the possible fundamental frequencies of the retuned string? (b) By what fractional amount was the string tension changed if it was (i) increased (ii) decreased?

A boy is walking away from a wall at a speed of $1.0 \mathrm{m} {\mathrm{s}}^{-1}$ in a direction at right angles to the wall. As he walks, he blows a whistle steadily. An observer towards whom the boy is walking hears $4.0$ beats per second. If the speed of sound is $340 \mathrm{m} {\mathrm{s}}^{-1}$, what is the frequency of the whistle?

Sound waves from a tuning fork $A$ reach a point $P$ by two separate paths $ABP$ and $ACP.$ When $ACP$ is greater than $ABP$ by $11.5 \mathrm{cm}$, there is a silence at $P.$ When the difference is $23 \mathrm{cm}$, the sound becomes loudest at $P$ and when $34.5 \mathrm{cm}$, there is a silence again and so on. Calculate the minimum frequency of the fork if the velocity of sound is taken to be $331.2 \mathrm{m} {\mathrm{s}}^{-1}$.