How long will a sound wave take to travel 1.5km, which has a frequency of 5 kHz and wavelength of 6 cm?

Correct — B. Find the speed first, then the time.

v = f × λ (wave speed = frequency × wavelength)
f = 5 kHz = 5000 Hz, λ = 6 cm = 0.06 m
v = 5000 × 0.06 = 300 m/s

t = distance ⁄ speed
= 1.5 km ⁄ 300 m/s = 1500 ⁄ 300
= 5 seconds → option (b)

Why the others are wrong

• (a)
  25 seconds — 25 is 1.5 ⁄ 0.06 — the distance left in kilometres and divided by the wavelength, with the frequency never used at all. Convert to metres and multiply f by λ before dividing.
• (c)
  50 seconds — 50 follows from λ = 0.006 m, that is, 6 cm converted as though a centimetre were a thousandth of a metre. It is a hundredth, so λ = 0.06 m and v = 300 m/s, not 30 m/s.
• (d)
  2.5 seconds — 2.5 s is the answer halved, and it comes from a speed of 600 m/s or from using 750 m in place of the full distance. The item gives 1.5 km, which is 1500 m.

Every wave obeys v = f λ. Speed, frequency and wavelength are locked together, so any two of them give the third.

The stem hands you two of them and hides the third inside a second formula — here time = distance ⁄ speed — so the item is two short steps, not one.

The marks are lost in the units. A kilohertz is a thousand hertz and a centimetre is a hundredth of a metre, and every wrong option in this item is a unit slip rather than a physics error.

Key facts

• For any wave, speed = frequency × wavelength.
• 1 kHz = 1000 Hz and 1 cm = 0.01 m.
• Sound travels at roughly 343 m/s in air at 20 °C, faster in water and faster still in steel.
• Time = distance ⁄ speed, so distance and speed must share the same length unit before you divide.

Common traps

• Converting 6 cm to 0.006 m and landing on 50 seconds.
• Dividing 1.5 by 0.06 without turning kilometres into metres, which gives 25.
• Stopping at the speed of 300 m/s when the item asks for the time.

No directly related past PYQ was found.