Chapter 18

Vibrations from a $622-\mathrm{Hz}$ tuning fork set up standing waves in a string clamped at both ends. The wave speed for the string is $388\mathrm{m}/\mathrm{s}$. The standing wave has four loops and an amplitude of $1.90\mathrm{mm}.$ (a) What is the length of the string? (b) Write an equation for the displacement of the string as a function of position and time.

A $15.0-\mathrm{cm}$ violin string, fixed at both ends, is vibrating in its $n=1$ mode. The speed of waves in this wire is $250\mathrm{m}/\mathrm{s}$, and the speed of sound in air is $348\mathrm{m}/\mathrm{s}$. What are $(a)$ the frequency and $(b)$ the wavelength of the emitted sound wave?

What are the three lowest frequencies for standing waves on a wire $9.88\mathrm{m}$ long having a mass of $0.107\mathrm{kg}$, which is stretched under a tension of $236\mathrm{N}?$

A $1.48$ -m-long wire has a mass of $8.62\mathrm{g}$ and is held under a tension of $122\mathrm{N}$. The wire is held rigidly at both ends and set into vibration. Calculate $(a)$ the speed of waves on the wire, (b) the wavelengths of the waves that produce one- and twoloop standing waves on the wire, and ( $c$ ) the frequencies of the waves in $(b)$.