The speed $v$ of a transverse wave on a stretched wire is given by the expression $v\propto \sqrt{T}$

Where $\mathrm{T}$ is the tension in the wire.

A length of wire is stretched between two fixed point. The tension in the wire is $\mathrm{T}$. The wire is gently plucked from the middle. A stationary wave, of fundamental frequency $210 \mathrm{Hz}$, is produced.

The tension in the wire is now increased to $1.4 \mathrm{T}$. The percentage uncertainty in new tension is $8.0\%$. The length of the wire is unchanged. Calculate the new value for the fundamental frequency when the wire is plucked in the middle. Your answer must include the absolute uncertainty written to an appropriate number of significant figures.

(b) Explain why it is better to measure the distance across several nodes.

For sound waves of frequency $2500 \mathrm{Hz}$, it is found that two nodes are separated by $20 \mathrm{cm}$, with three antinodes between them.

(b) Use the wave equation $v=f\lambda$ to determine the speed of sound in air.

A tuning fork that produces a note of 256Hz is placed above a tube that is nearly filled with water. The water level is lowered until resonance is first heard.

(a) Explain what is meant by the term resonance.

(b) This diagram shows an experiment to measure the speed of a sound in a string. The frequency of the vibrator is adjusted until the stationary wave shown is formed.

(ii) The frequency of the vibrator is 120Hz. Calculate the speed at which a progressive wave would travel along the string.

This diagram shows a stationary wave, of frequency $400\mathrm{Hz}$, produced by a loudspeaker in a closed tube.

(a) Describe the movement of the air particles at:

(i) $\left(\mathrm{A}\right)$