If the speed of sound in a medium is 340 m/s and a sound wave has a frequency of 680 Hz, what is its wavelength?

Correct — A. Speed, frequency and wavelength are linked by v = fλ.

Rearrange for wavelength: λ = v ÷ f
Substitute: λ = 340 ÷ 680
Divide: λ = 0.5 m → option (a)

Check: 680 waves a second, each 0.5 m long, cover 680 × 0.5 = 340 m each second.

Why the others are wrong

• (b)
  2 m — 2 m comes from dividing the wrong way, 680 ÷ 340. That quotient is f ÷ v = 1⁄λ, the number of waves per metre, not the wavelength.
• (c)
  20 m — 20 m does not follow from these numbers. At 340 m/s a 20 m wavelength would need a frequency of 340 ÷ 20 = 17 Hz, not 680 Hz.
• (d)
  50 m — 50 m would need a frequency of 340 ÷ 50 = 6.8 Hz. It looks like 0.5 with the decimal point moved two places.

In one cycle a wave advances one wavelength (λ), and frequency (f) counts cycles per second. So the distance covered each second, the speed, is v = fλ.

In a given medium sound travels at a fixed speed, so frequency and wavelength are inversely related: raise one and the other falls. Here f = 680 Hz is double the speed's figure of 340, so λ is half a metre.

Key facts

• Wave equation: v = fλ, so λ = v ÷ f and f = v ÷ λ.
• 1 hertz (Hz) is one cycle per second.
• When sound passes from one medium into another, its frequency stays the same while its speed and wavelength change.
• The audible range for humans is roughly 20 Hz to 20,000 Hz.

Common traps

• Dividing 680 by 340 instead of 340 by 680, which gives 2 m.
• Forgetting that, at a fixed speed, a higher frequency means a shorter wavelength.

No directly related past PYQ was found.