Free Waves MCQs with Answers

1. In a transverse wave, the particles of the medium vibrate

• A. along the direction of propagation
• B. perpendicular to the direction of propagation
• C. in circles of increasing radius
• D. not at all

Explanation: Light, waves on a string and ripples on water are transverse, with the displacement at right angles to the direction the energy travels. In a longitudinal wave such as sound the vibration is along the direction of travel, producing compressions and rarefactions. Only transverse waves can be polarised, which is the standard experimental test of which type a wave is.

2. The relationship between the speed v, frequency f and wavelength of a wave is

• A. v equals f divided by wavelength
• B. v equals f times wavelength
• C. v equals wavelength divided by f
• D. v equals f plus wavelength

Explanation: In one period the wave advances exactly one wavelength, so dividing wavelength by period gives the speed, and since frequency is the reciprocal of period this becomes v equals f multiplied by wavelength. Speed is fixed by the medium, so raising the frequency shortens the wavelength in proportion. That inverse relationship is the point most questions turn on.

3. A wave of frequency 500 Hz travels at 340 m per second. Its wavelength is

• A. 0.68 m
• B. 1.47 m
• C. 170 m
• D. 0.34 m

Explanation: Wavelength is speed divided by frequency, so 340 divided by 500 gives 0.68 m. Multiplying instead of dividing produces the absurdly large 170 m, which a quick sanity check on audible sound would rule out. Middle C at about 262 Hz has a wavelength of roughly 1.3 m, which is a useful reference point.

4. The speed of sound is greatest in

• A. air
• B. water
• C. steel
• D. vacuum

Explanation: Sound travels fastest in solids because their particles are closely bound and pass on a disturbance quickly, giving about 5000 m per second in steel against 1500 in water and 340 in air. It cannot travel through a vacuum at all, since it needs a material medium. Light behaves in exactly the opposite way, travelling fastest in a vacuum.

5. The speed of sound in air increases when

• A. the pressure alone increases at constant temperature
• B. the temperature increases
• C. the humidity falls
• D. the frequency of the sound increases

Explanation: Speed rises by roughly 0.61 m per second for every degree Celsius, because hotter molecules move faster and transmit the disturbance more quickly. Changing pressure alone has no effect, since density changes in the same proportion and the two cancel. Speed is also independent of frequency, which is why a distant band is heard in tune rather than smeared out.

6. The principle of superposition states that when two waves meet, the resultant displacement at any point is

• A. the vector sum of the individual displacements
• B. always zero
• C. always double one of them
• D. the larger of the two displacements

Explanation: Displacements add algebraically, so waves in phase reinforce and waves in antiphase cancel, and afterwards each wave continues unchanged. This single principle underlies interference, beats and stationary waves alike. Cancellation is only complete when the two amplitudes are equal as well as opposite.

7. For two sources to produce a steady, observable interference pattern they must be

• A. of different frequencies
• B. coherent, keeping a constant phase relationship
• C. very far apart
• D. of unequal amplitude

Explanation: If the phase difference between the sources drifts, the positions of the bright and dark fringes shift too fast to be seen and the pattern washes out. Coherence in practice means the same frequency and a fixed phase relationship, which is why Young used a single source split into two rather than two separate lamps. Equal amplitudes are not required, but they give the greatest contrast.

8. Constructive interference occurs when the path difference between two coherent waves is

• A. an odd number of half wavelengths
• B. a whole number of wavelengths
• C. always zero
• D. one quarter of a wavelength

Explanation: A path difference of a whole number of wavelengths brings the waves back into phase, so the crests coincide and the amplitude is a maximum. An odd number of half wavelengths puts them in antiphase and gives destructive interference. Zero path difference is simply the special case of the central maximum.

9. Beats are produced when two sound waves

• A. of exactly the same frequency overlap
• B. of slightly different frequencies overlap
• C. travel in opposite directions
• D. have very different amplitudes

Explanation: The two waves drift in and out of phase, so the loudness rises and falls at a rate equal to the difference between the two frequencies. A piano tuner uses this directly, tightening a string until the beats slow to nothing and the note matches the fork. Waves of exactly the same frequency give a steady sound rather than beats.

10. Two tuning forks of 256 Hz and 260 Hz are sounded together. The beat frequency is

• A. 4 Hz
• B. 258 Hz
• C. 516 Hz
• D. 0.5 Hz

Explanation: The beat frequency is simply the difference between the two frequencies, so 260 minus 256 gives 4 beats per second. Their average, 258 Hz, is the pitch actually heard, which is why it appears as a distractor. Beats become too rapid to distinguish once the difference exceeds about 10 Hz.