Advertisements
Advertisements
प्रश्न
A sonometer wire is vibrating in resonance with a tuning fork. Keeping the tension applied same, the length of the wire is doubled. Under what conditions would the tuning fork still be is resonance with the wire?
उत्तर
Wire of twice the length vibrates in its second harmonic. Thus, if the tuning fork resonates at L it will resonate at 2 L This can be explained below The sonometer frequency is given by
`v = n/(2L) sqrt(T/m)` .....(n = number of loops)
Now, as it vibrates with length L, we assume `v = v_1`
`n = n_1`
∴ `v_1 = n_1/(2L) sqrt(T/m)` ......(i)
When length is doubled, then `v_2 = n_2/(2 xx 2L) sqrt(T/m)` ......(ii)
Dividing equation (i) by equation (ii), we get
`v_1/v_2 = n_1/n_2 xx 2`
To keep the resonance `v_1/v_2 = 1 = n_1/n_2 xx 2`
⇒ `n_2 = 2n_1`
Hence, when the wire is doubled the number of loops also gets doubled to produce the resonance. That is it resonates in the second harmonic.
APPEARS IN
संबंधित प्रश्न
An open organ pipe of length L vibrates in its fundamental mode. The pressure variation is maximum
The transverse displacement of a string (clamped at its both ends) is given by y(x, t) = 0.06 sin (2πx/3) cos (120 πt). All the points on the string between two consecutive nodes vibrate with ______.
- same frequency
- same phase
- same energy
- different amplitude.
Which of the following statements are true for a stationary wave?
- Every particle has a fixed amplitude which is different from the amplitude of its nearest particle.
- All the particles cross their mean position at the same time.
- All the particles are oscillating with same amplitude.
- There is no net transfer of energy across any plane.
- There are some particles which are always at rest.
The wave pattern on a stretched string is shown in figure. Interpret what kind of wave this is and find its wavelength.
Show that when a string fixed at its two ends vibrates in 1 loop, 2 loops, 3 loops and 4 loops, the frequencies are in the ratio 1:2:3:4.
Two identical strings X and Z made of same material have tension Tx and Tz in them If their fundamental frequencies are 450 Hz and 300 Hz, respectively, then the ratio `"T"_x/"T"_"z"` is ______.
Shown in the figure is rigid and uniform one meter long rod AB held in horizontal position by two strings tied to its ends and attached to the ceiling. The rod is of mass 'm' and has another weight of mass 2m hung at a distance of 75 cm from A. The tension in the string at A is :
Two travelling waves produce a standing wave represented by the equation. y = 1.0 mm cos (1.57 cm-1) x sin (78.5 s-1)t. The node closest to the origin in the region x > 0 will be at x = ______ cm.
A wire of length 2L is made by joining two wires A and B of the same length but different radii r and 2r, and made of the same material. It is vibrating at a frequency such that the joint of the two wires forms a node. If the number of antinodes in wire A is p and that in B is q then the ratio p : q is ______.
A string 2.0 m long and fixed at its ends is driven by a 240 Hz vibrator. The string vibrates in its third harmonic mode. The speed of the wave and its fundamental frequency is ______.
