AS 91523 · 2023 paper · Sam's violin

Question 1(c) Merit

A violin's strings are fixed at both ends, 0.331 m apart, and Sam makes them vibrate with a bow. One string, the "G", plays a fundamental frequency of 196 Hz. Assume the speed of sound in air is 342 m s⁻¹.

L	0.331 m
f₁	196 Hz
v sound	342 m s⁻¹

Sam plays the violin (fundamental 196 Hz) sitting on a trailer that moves at 5.30 m s⁻¹ directly towards microphone A.

Calculate the frequency recorded by microphone A.

The 2023 paper, page 3 ↗ Marking schedule, page 1 ↗

See it move: The Doppler effect: a moving source and a moving observer

Work it out

Try it on paper first. Stuck? Take one hint at a time.

1 Who is moving, and which way?
The source, the violin, moves towards microphone A, and the microphone is still: the moving-source formula, approaching.
2 Which speed goes in the formula: the wave on the string, or the sound in the air?
The sound in the air, 342 m s⁻¹: the air carries the sound to the microphone. The 130 m s⁻¹ from (a) belongs to the string.
3 Put the values in.
f′ = f × v / (v − v_s) = 196 × 342 / (342 − 5.30) = 196 × 342 / 336.7 = 199.09 Hz

Answer 199 Hz (199.09 Hz unrounded): a little above 196 Hz, as the violin comes towards A.

What the marker wanted

Achieved The values put correctly into the right equation.
Merit The right frequency, 199 Hz.

In our words, from NZQA’s 2023 marking schedule.

Common mistake

Using 130 m s⁻¹, the string’s wave speed from (a), as the speed of sound. The schedule gives that substitution Achieved only: the sound reaches the microphone through the air, at 342 m s⁻¹.

How did it go?

Got it moves it further out. Review brings it back tomorrow.