Advertisements
Advertisements
Question
A particular guitar wire is 30⋅0 cm long and vibrates at a frequency of 196 Hz when no finger is placed on it. The next higher notes on the scale are 220 Hz, 247 Hz, 262 Hz and 294 Hz. How far from the end of the string must the finger be placed to play these notes?
Advertisements
Solution
Given:
Length of the guitar wire (L1) = 30.0 cm = 0.30 m
Frequency, when no finger is placed on it, (f1) =196 Hz
And (f2) =220 Hz, (f3) = 247 Hz, (f4) = 262 Hz and (f5) = 294 Hz
The velocity is constant for a medium.
We have:
\[f \propto \left( \frac{1}{L} \right)\]
\[\Rightarrow \frac{f_1}{f_2} = \frac{L_2}{L_1}\]
\[ \Rightarrow \frac{196}{220} = \frac{L_2}{0 . 3}\]
\[ \Rightarrow L_2 = \frac{196 \times 0 . 3}{220} = 0 . 267 m\]
\[ \Rightarrow L_2 = 26 . 7 cm\]
Again,
\[f_3 = 247 Hz\]
\[\Rightarrow \frac{f_3}{f_1} = \frac{L_1}{L_3}\]
\[ \Rightarrow \frac{247}{196} = \frac{0 . 3}{L_3}\]
\[ \Rightarrow L_3 = 196 \times \frac{0 . 3}{247} = 0 . 238 m\]
\[ \Rightarrow L_3 = 23 . 8 cm\]
\[Similarly, L_4 = 196 \times \frac{0 . 3}{262} = 0 . 224 m\]
\[ \Rightarrow L_4 = 22 . 4 cm\]
\[And, L_5 = 20 \text{ cm }\]
APPEARS IN
RELATED QUESTIONS
If you are walking on the moon, can you hear the sound of stones cracking behind you? Can you hear the sound of your own footsteps?
A tuning fork sends sound waves in air. If the temperature of the air increases, which of the following parameters will change?
A tuning fork of frequency 512 Hz is vibrated with a sonometer wire and 6 beats per second are heard. The beat frequency reduces if the tension in the string is slightly increased. The original frequency of vibration of the string is
A small source of sounds moves on a circle as shown in figure and an observer is sitting at O. Let \[v_1, v_2, v_3\] be the frequencies heard when the source is at A, B and C respectively.
An electrically maintained tuning fork vibrates with constant frequency and constant amplitude. If the temperature of the surrounding air increases but pressure remains constant, the produced will have
(a) larger wavelength
(b) larger frequency
(c) larger velocity
(d) larger time period.
The fundamental frequency of a vibrating organ pipe is 200 Hz.
(a) The first overtone is 400 Hz.
(b) The first overtone may be 400 Hz.
(c) The first overtone may be 600 Hz.
(d) 600 Hz is an overtone.
A string, fixed at both ends, vibrates in a resonant mode with a separation of 2⋅0 cm between the consecutive nodes. For the next higher resonant frequency, this separation is reduced to 1⋅6 cm. Find the length of the string.
The noise level in a classroom in absence of the teacher is 50 dB when 50 students are present. Assuming that on the average each student output same sound energy per second, what will be the noise level if the number of students is increased to 100?
A source S and a detector D are placed at a distance d apart. A big cardboard is placed at a distance \[\sqrt{2}d\] from the source and the detector as shown in figure. The source emits a wave of wavelength = d/2 which is received by the detector after reflection from the cardboard. It is found to be in phase with the direct wave received from the source. By what minimum distance should the cardboard be shifted away so that the reflected wave becomes out of phase with the direct wave?
The two sources of sound, S1 and S2, emitting waves of equal wavelength 20.0 cm, are placed with a separation of 20.0 cm between them. A detector can be moved on a line parallel to S1 S2 and at a distance of 20.0 cm from it. Initially, the detector is equidistant from the two sources. Assuming that the waves emitted by the sources are in detector should be shifted to detect a minimum of sound.
Two coherent narrow slits emitting sound of wavelength λ in the same phase are placed parallel to each other at a small separation of 2λ. The sound is detected by moving a detector on the screen ∑ at a distance D(>>λ) from the slit S1 as shown in figure. Find the distance x such that the intensity at P is equal to the intensity at O.
A heavy string is tied at one end to a movable support and to a light thread at the other end as shown in following figure. The thread goes over a fixed pulley and supports a weight to produce a tension. The lowest frequency with which the heavy string resonates is 120 Hz. If the movable support is pushed to the right by 10 cm so that the joint is placed on the pulley, what will be the minimum frequency at which the heavy string can resonate?
A source of sound with adjustable frequency produces 2 beats per second with a tuning fork when its frequency is either 476 Hz of 480 Hz. What is the frequency of the tuning fork?
A piano wire A vibrates at a fundamental frequency of 600 Hz. A second identical wire Bproduces 6 beats per second with it when the tension in A is slightly increased. Find the the ratio of the tension in A to the tension in B.
For the propagation of longitudinal waves, the medium must have
- elasticity
- mass
- inertia
- force of cohesion
The speed of a wave in a string is 20 m/s and the frequency is 50 Hz. The phase difference between two points on the string 10 cm apart will be ______.
A small speaker delivers 2W of audio output. At what distance from the speaker will one detect 120 dB intensity sound?
[Given reference intensity of sound as 10-12W/m2]
