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
A string clamped at both ends vibrates in its fundamental mode. Is there any position (except the ends) on the string which can be touched without disturbing the motion? What if the string vibrates in its first overtone?
The voice of a person, who has inhaled helium, has a remarkably high pitch. Explain on the basis of resonant vibration of vocal cord filled with air and with helium.
Two tuning forks vibrate with the same amplitude but the frequency of the first is double the frequency of the second. Which fork produces more intense sound in air?
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.
If the intensity of sound is doubled, by how many decibels does the sound level increase?
Sound with intensity larger than 120 dB appears pain full to a person. A small speaker delivers 2.0 W of audio output. How close can the person get to the speaker without hurting his ears?
If the sound level in a room is increased from 50 dB to 60 dB, by what factor is the pressure amplitude increased?
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 uniform horizontal rod of length 40 cm and mass 1⋅2 kg is supported by two identical wires as shown in figure. Where should a mass of 4⋅8 kg be placed on the rod so that the same tuning fork may excite the wire on left into its fundamental vibrations and that on right into its first overtone? Take g = 10 m s−2.
A source of sound S and detector D are placed at some distance from one another. a big cardboard is placed near hte detector and perpendicular to the line SD as shown in figure. It is gradually moved away and it is found that the intensity changes from a maximum to a minimum as the board is moved through a distance of 20 cm. Find the frequency of the sound emitted. Velocity of sound in air is 336 m s−1.
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?
In a standing wave pattern in a vibrating air column, nodes are formed at a distance of 4.0 cm. If the speed of sound in air is 328 m s−1, what is the frequency of the source?
The separation between a node and the next antinode in a vibrating air column is 25 cm. If the speed of sound in air is 340 m s−1, find the frequency of vibration of the air column.
Two electric trains run at the same speed of 72 km h−1 along the same track and in the same direction with separation of 2.4 km between them. The two trains simultaneously sound brief whistles. A person is situated at a perpendicular distance of 500 m from the track and is equidistant from the two trains at the instant of the whistling. If both the whistles were at 500 Hz and the speed of sound in air is 340 m s−1, find the frequencies heard by the person.
A small source of sound oscillates in simple harmonic motion with an amplitude of 17 cm. A detector is placed along the line of motion of the source. The source emits a sound of frequency 800 Hz which travels at a speed of 340 m s−1. If the width of the frequency band detected by the detector is 8 Hz, find the time period of the source.
Equation of a plane progressive wave is given by `y = 0.6 sin 2π (t - x/2)`. On reflection from a denser medium its amplitude becomes 2/3 of the amplitude of the incident wave. The equation of the reflected wave is ______.
In the wave equation
`y = 0.5sin (2pi)/lambda(400t - x)m`
the velocity of the wave will be ______.
