Question

In a medium, a source produces 60 crests and 60 troughs in a time of 0.2 s. If the distance between a crest and its adjacent trough is 100 cm, then the speed of sound in the medium is:

• A. $600\ \mathrm{m\,s^{-1}}$
• B. $1200\ \mathrm{m\,s^{-1}}$
• C. $300\ \mathrm{m\,s^{-1}}$
• D. $200\ \mathrm{m\,s^{-1}}$

Hint:

Remember: crest-to-adjacent-trough distance = $\lambda/2$.
Count crests (or cycles) per unit time to get frequency.
Wave speed $v = f\lambda$ connects frequency and wavelength directly.
Always convert cm to meters for SI consistency.

Answer 1

The Correct Option is A

• One full cycle contains one crest and one trough. The presence of 60 crests and 60 troughs in 0.2 s corresponds to 60 full cycles in 0.2 s.
• Frequency $f = \dfrac{60}{0.2} = 300\ \mathrm{Hz}$.
• Distance between crest and adjacent trough $= \dfrac{\lambda}{2} = 100\ \text{cm} = 1\ \mathrm{m}$.
• Hence wavelength $\lambda = 2\ \mathrm{m}$.
• Speed $v = f\lambda = 300 \times 2 = 600\ \mathrm{m\,s^{-1}}$.
• Therefore the speed of sound in the medium is $600\ \mathrm{m\,s^{-1}$}.