Waves

The speed of the sound emitted by the loudspeaker is $330\ \text{m s}^{-1}$.

Determine the wavelength of the sound.

wavelength = ______ $\text{m}$

The loudspeaker now moves in a straight line while emitting the same sound of constant frequency. The period of the trace on the CRO increases continuously.

Describe the motion of the loudspeaker.

Use the definitions of speed $v$, frequency $f$ and wavelength $\lambda$ to derive the wave equation

Calculate the frequency of the sound waves detected by the microphone.

frequency = ______ $\text{Hz}$

Determine the speed of the sound in air.

speed of sound = ______ $\text{m s}^{-1}$

State why sound waves cannot be polarised.

On Fig. 5.2, sketch the variation of the intensity $I$ of the transmitted light with the angle of rotation $\alpha$ as the filter is rotated through $360^{\circ}$ from its initial position.

The amplitude of the incident light wave is $A_0$ when the intensity of the wave is $I_0$.

Use Malus’s law to determine, in terms of $A_0$, the amplitude of the transmitted wave when $\alpha = 20^{\circ}$.

amplitude = ______ $A_0$

By reference to the direction of propagation of energy, state what is meant by a transverse wave.

A space telescope is designed to detect electromagnetic radiation with wavelengths in the range $12\ \mu\text{m}$ to $28\ \mu\text{m}$.

State the region of the electromagnetic spectrum for this radiation.

A detector on another space telescope detects an electromagnetic wave. The signal from the detector is transmitted to Earth and displayed on an oscilloscope as shown in Fig. 5.1. The frequency of the signal displayed on the oscilloscope is equal to the frequency of the detected electromagnetic wave.

The time-base setting on the oscilloscope is $5.0 \times 10^{-15}\ \text{s cm}^{-1}$.

Calculate the wavelength of the detected electromagnetic wave.

wavelength = ______ $\text{m}$

On Fig. 5.2, sketch the variation of the frequency of sound heard by the observer with time $t$,
from time $t = 0$ to $t = t_2$.

At a particular time, the sound waves at the observer have an intensity of $4.7 \times 10^{-3}\ \text{W m}^{-2}$.
The waves at the observer are incident at right angles on a circular detector of radius $2.8\ \text{cm}$.

Calculate the power $P$ of the waves incident on the detector.

$P$ = ______ $\text{W}$

Calculate the speed of the train.

speed = ______ $\text{m s}^{-1}$

State the relationship between amplitude $A$ and intensity $I$ for a progressive wave.

On Fig. 6.3, sketch the variation with $d/x_0$ of $A/A_0$.

Calculate the minimum frequency, to three significant figures, of the sound heard by the observer.

minimum frequency = ______ $\text{Hz}$

The circular path of the source has a radius of $2.4\ \text{m}$.

Determine the shortest time interval between the observer hearing sound of minimum frequency and the observer hearing sound of maximum frequency.

time interval = ______ $\text{s}$

By reference to the direction of transfer of energy, state what is meant by a longitudinal wave.

Explain why the frequency of the sound detected by the observer is sometimes above and sometimes below $1.2\text{ kHz}$.

State the name of the phenomenon in (b)(i).

On Fig. 4.1, mark with a letter X the position of the vehicle when it emitted the sound that is detected at time $T$.

On Fig. 4.1, mark with a letter Y the position of the vehicle when it emitted the sound that is detected at time $\frac{9T}{4}$.

The speed of the sound in the air is $320\text{ m s}^{-1}$.

Use Fig. 4.2 to determine the speed of the vehicle in (b).

speed = ______ $\text{m s}^{-1}$

from time $t = 0$ to time $t = 2.0\ \text{s}$

from time $t = 4.0\ \text{s}$ to time $t = 6.0\ \text{s}$.

Determine the frequency, to three significant figures, of the sound heard, by the child, that was emitted from the car horn at time $t = 3.0\ \text{s}$.

frequency = ______ $\text{Hz}$

Determine the time taken for the sound emitted at time $t = 4.0\ \text{s}$ to travel to the child.

time taken = ______ $\text{s}$

Determine the speed of the wave.

speed = ______ $\text{m s}^{-1}$

A second wave Z has wavelength $8.0\ \text{cm}$ and amplitude $2.0\ \text{mm}$ at point P. Waves Y and Z have the same speed.

For the waves at point P, calculate the ratio

ratio = ______