Question

The frequency of a tuning fork is 'n' Hz and velocity of sound in air is 'V' m/s. When the tuning fork completes 'x' vibrations, the distance travelled by the wave is

• A. $\frac{Vx}{n}$
• B. $\frac{Vn}{x}$
• C. $\frac{xV}{n}$
• D. $\frac{x}{Vn}$

Hint:

Alternatively, look at the wavelength definition: the distance travelled during exactly one full vibration cycle is one wavelength ($\lambda = \frac{V}{n}$). Therefore, the total distance covered across a span of $x$ cycles is simply $x \cdot \lambda = \frac{xV}{n}$!

Answer 1

The Correct Option is A

The time period ($T$) required for a tuning fork to complete exactly one single vibration is the reciprocal of its frequency: $$T = \frac{1}{n}$$ The total time ($t$) taken to complete a sequence of $x$ independent vibrations is: $$t = x \cdot T = \frac{x}{n}$$ Since a sound wave travels through a medium at a constant uniform velocity $V$, the total linear distance ($d$) propagated during this time frame is: $$d = \text{Velocity} \times \text{Time} = V \cdot t = \frac{Vx}{n}$$
Final Answer:
The total distance travelled by the wave is $\frac{Vx}{n}$, which corresponds to option (A).