A string 1m long is drawn by a 300 Hz vibrator attached to its end. The string vibrates in three segments. The speed of transverse waves in the string is equal to

Options

A. `100 m//s`
B. `200 m//s`
C. `300 m//s`
D. `400 m//s`

Explanation

To find the speed of transverse waves in a string that is vibrating in three segments, we can use the relationship between frequency, wavelength, and wave speed. Here’s the step-by-step solution:

### Step 1: Understand the given information
- Length of the string (L) = 1 meter
- Frequency of the vibrator (f) = 300 Hz
- The string vibrates in three segments, which indicates that it is in the third harmonic (n = 3).

### Step 2: Determine the fundamental frequency
The fundamental frequency (f₀) of a string fixed at both ends is given by:
\[ f₀ = \frac{v}{2L} \]
where v is the speed of the wave in the string.

### Step 3: Relate the harmonic frequency to the fundamental frequency
For the nth harmonic, the frequency is given by:
\[ f_n = n \cdot f₀ \]
In this case, since the string vibrates in three segments (n = 3):
\[ f_3 = 3 \cdot f₀ \]

### Step 4: Substitute the known frequency
We know that:
\[ f_3 = 300 \text{ Hz} \]
Thus:
\[ 300 = 3 \cdot f₀ \]

### Step 5: Solve for the fundamental frequency
Now, we can find the fundamental frequency:
\[ f₀ = \frac{300}{3} = 100 \text{ Hz} \]

### Step 6: Use the fundamental frequency to find the wave speed
Now we can use the relationship between the fundamental frequency and wave speed:
\[ f₀ = \frac{v}{2L} \]
Substituting the values we have:
\[ 100 = \frac{v}{2 \cdot 1} \]

### Step 7: Solve for the speed of the wave
Rearranging the equation to solve for v:
\[ v = 100 \cdot 2 = 200 \text{ m/s} \]

### Conclusion
The speed of transverse waves in the string is:
\[ v = 200 \text{ m/s} \]

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