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

Step 1: Time for one vibration.
The period is $T=\frac{1}{n}$.

Step 2: Time for $x$ vibrations.
The total time is $t=xT=\frac{x}{n}$.

Step 3: Distance travelled by the wave.
The wave moves at speed $V$, so $d=Vt=\frac{Vx}{n}$. \[ \boxed{\frac{Vx}{n}} \]