Question

The frequency of a tuning fork is $220 \text{ Hz}$ and the velocity of sound in air is $330 \text{ m/s}$. When the tuning fork completes $80$ vibrations, the distance travelled by the sound wave is

• A. $120 \text{ m}$
• B. $60 \text{ m}$
• C. $53 \text{ m}$
• D. $100 \text{ m}$

Hint:

You can set this up as a direct time-substitution shortcut! The time for $N$ vibrations is $t = \frac{N}{f}$. Substituting this into the classic distance formula $d = v \cdot t$ gives $d = v \cdot \left(\frac{N}{f}\right) = 330 \cdot \left(\frac{80}{220}\right) = 1.5 \times 80 = 120 \text{ m}$ in a single sequence.

Answer 1

The Correct Option is A

Step 1: Understanding the Question:
The problem presents a source generating a sound wave at a specific frequency and propagation speed. We need to determine the total physical distance the wave front travels through the air medium in the time it takes the tuning fork to execute exactly 80 complete structural vibrations.

Step 2: Key Formula or Approach:
The distance traveled by a wave during a single full vibration cycle is equal to exactly one wavelength ($\lambda$). Therefore, the total distance $d$ covered over $N$ vibrations is:
$$d = N \cdot \lambda$$ The wavelength $\lambda$ can be determined from the fundamental wave equation linking velocity $v$ and frequency $f$:
$$v = f \cdot \lambda \implies \lambda = \frac{v}{f}$$

Step 3: Detailed Explanation:
Let's list the given parameters:
Frequency, $f = 220 \text{ Hz}$
Velocity of sound, $v = 330 \text{ m/s}$
Number of vibrations, $N = 80$
First, calculate the spatial wavelength ($\lambda$) of the sound wave:
$$\lambda = \frac{330}{220} = \frac{3}{2} = 1.5 \text{ m}$$ Next, compute the cumulative distance traveled over 80 cycles by multiplying the number of vibrations by the wavelength:
$$d = 80 \times 1.5 \text{ m} = 80 \times \frac{3}{2} = 40 \times 3 = 120 \text{ m}$$

Step 4: Final Answer:
The distance travelled by the sound wave is $120 \text{ m}$, which corresponds to option (A).