Page 130 - Physics - XI

Table for calculation of frequency and resonant length

Resonant length of the wire l (cm)
Frequency of Product

S. No. tuning fork Length Length Mean 1/l –1 n.l
n (Hz) increasing decreasing l l l 2 (cm) (cm ) (Hz. cm)
1
l (cm) l (cm) 2
1 2
1.
2.
3.
4.
5.
6.

Graph Y
1
1. Plot a graph between and frequency n of the tuning fork,
l 1
taking n along X-axis and along Y-axis. It will be a straight
l
line as shown in Fig. 8.3.
2. The product n × l = constant for all observations within the 1/l (cm –1 ) Scale used on:

experimental error. X-axis, 1 cm = ... Hz –1
Y-axis, 1 cm = ... cm
Result
1. We fi nd that within the experimental error, the product of X
resonant length l and the frequency n is constant. This verifi es n (Hz)
1
1 Fig. 8.3: Variation of with n
that n ∝ l
l
1
2. The graph plotted between n and 1/l is a straight line as shown in Fig. 8.3, we conclude that n ∝ .
l
This verifi es law of length of transverse vibrations of strings.

Precautions

1. The wire should be free from kinks.
2. The wire should have uniform area of cross-section throughout.
3. The pulley should be frictionless.
4. The wire should not be loaded beyond the elastic limit.

5. The paper rider should always be kept in the middle of the wire between the bridges.
6. While fi nding the resonant length, start with a small distance between the bridges.
7. The stem of the tuning fork should be placed gently on the top of the sonometer box.
8. The weight of the hanger should be counted for the calculation of the tension on the string.

Sources of Error

1. Wire may not have uniform area of cross-section.
2. Pulley may not be frictionless.
3. Bridges may not be sharp.

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