In a sonometer experiment, resonance occurs when the length of the wire between bridges is 20 cm and a tuning fork of frequency 300 Hz excites the vibrations. If a tuning fork of frequency 400 Hz is used, then the resonant length of the wire will be

• A. 10 cm
• B. 15 cm
• C. 20 cm
• D. 25 cm

In a sonometer experiment, resonance is achieved when the frequency of the tuning fork matches the natural frequency of the vibrating wire. The relationship between the frequency and the length of the wire can be described by the formula:

Frequency and Length Relationship

The frequency of vibration is inversely proportional to the length of the wire. This means that if the frequency increases, the length must decrease to maintain resonance. The formula can be expressed as:

• f ∝ 1/L

Calculating the New Length

Given that the initial length (L1) is 20 cm for a frequency (f1) of 300 Hz, we can find the new length (L2) for a frequency (f2) of 400 Hz using the ratio:

• f1 / f2 = L2 / L1

Substituting the known values:

• 300 Hz / 400 Hz = L2 / 20 cm

Cross-multiplying gives:

• 300 * 20 = 400 * L2

This simplifies to:

• 6000 = 400 * L2

Solving for L2:

• L2 = 6000 / 400 = 15 cm

Final Answer

Thus, when using a tuning fork of frequency 400 Hz, the resonant length of the wire will be 15 cm. Therefore, the correct option is B. 15 cm.