Free Wave Speed MCQs with Answers

1. 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.

2. 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.

3. The Doppler effect explains why the pitch of an approaching ambulance siren sounds

• A. lower than the true pitch
• B. higher than the true pitch, because the waves reach the observer more frequently
• C. unchanged
• D. louder but of the same pitch

Explanation: Motion towards the observer crowds the wavefronts together, shortening the observed wavelength and raising the frequency, and the pitch drops abruptly as the source passes and begins to recede. The speed of sound in the air is unchanged throughout; only the observed frequency shifts. The same effect on light gives the red shift used to measure the recession of galaxies.