Question on waves and vibrations

In summary, the person in the room will experience a maximum sound intensity of 105 dB and a minimum sound intensity of 86 dB as he moves around due to the constructive and destructive interference of the two sound sources emitting frequencies of 100 dB and 98 dB. The extremal conditions can be determined by adding or subtracting the individual amplitudes and converting the result to dB.
  • #1
the_godfather
22
0

Homework Statement



this is part of a problem sheet and is the last question i have left to work out. i have been given solutions of 105dB and 86dB.

A person is in a room in which two sources of sound of loudness 100 dB and
98 dB are emitting the same frequency. The sources form a standing wave pattern in the room. What are the maximum and minimum loudness the person will be subjected to as he moves about?


Homework Equations





The Attempt at a Solution



not to sure i understand the question. i think it asks what is the constructive and destructive superposition that can occur. if so, what is my next step
i'm guessing that the Standing wave ratio formula is a part of this but what is the amplitude reflection co-eff?

thanks
 
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  • #2
If the two sound waves interfere entirely constructively, their amplitudes (intensities) will simply add together. If they interfere entirely destructively, their amplitudes (intensities) will subtract. Therefore, these are the extremal conditions, i.e. the represent the maximum and minimum possible sound intensities the person can hear. Of course, first you have to figure out what the individual amplitudes are, then add or subtract them, then see what the result is in dB.
 
  • #3


I would approach this question by first understanding the concepts of waves and vibrations. In this scenario, we have two sources of sound emitting the same frequency, which means they are in phase and will create a standing wave pattern in the room. A standing wave is formed when two waves with the same frequency and amplitude travel in opposite directions and interfere with each other, resulting in stationary points (nodes) and points of maximum displacement (antinodes).

The loudness of a sound is measured in decibels (dB) and is a relative measure of the intensity of the sound. In this case, the person in the room will experience different loudness levels as they move about due to the constructive and destructive interference of the two sound sources. The maximum loudness will occur at the antinodes, where the two waves are in phase and reinforce each other, resulting in a louder sound. The minimum loudness will occur at the nodes, where the two waves are out of phase and cancel each other out, resulting in a quieter sound.

To calculate the maximum and minimum loudness, we can use the formula for sound intensity level, which is measured in dB and is given by:

β = 10log(I/I0)

Where β is the sound intensity level, I is the sound intensity, and I0 is the reference intensity (usually taken as 10^-12 W/m^2).

Since we are given the loudness levels of the two sound sources (100 dB and 98 dB), we can use the above equation to calculate the corresponding sound intensities (I1 and I2). Then, using the principle of superposition, we can add these two intensities to determine the maximum and minimum loudness levels experienced by the person in the room.

The next step would be to calculate the amplitude reflection coefficient, which is a measure of how much of the incident sound is reflected at the boundary of the room. This will depend on the properties of the room and can be calculated using the room's dimensions, material properties, and the frequency of the sound. Once we have this coefficient, we can use the standing wave ratio formula to determine the constructive and destructive interference that occurs at different locations in the room.

In conclusion, the maximum and minimum loudness levels experienced by the person in the room can be calculated using the principles of sound intensity level, superposition, and standing wave ratio. Understanding these concepts and using the appropriate formulas will help
 

FAQ: Question on waves and vibrations

1. What are waves and vibrations?

Waves and vibrations are disturbances that propagate through a medium, transferring energy without permanently displacing the medium itself. Vibrations are oscillations that move back and forth, while waves are disturbances that travel through a medium.

2. What causes waves and vibrations?

Waves and vibrations can be caused by various sources such as sound, earthquakes, electromagnetic radiation, and even movement of particles at the atomic level. They can also be created by artificial means, such as with musical instruments or machinery.

3. What are the properties of waves and vibrations?

The properties of waves and vibrations include amplitude, wavelength, frequency, and velocity. Amplitude is the maximum displacement of a wave, while wavelength is the distance between two peaks or troughs. Frequency is the number of waves that pass a given point in a certain amount of time, and velocity is the speed at which the wave propagates.

4. How are waves and vibrations measured?

Waves and vibrations can be measured using various instruments such as oscilloscopes, seismographs, and spectrophotometers. The measurements taken depend on the specific properties of the wave being studied, such as amplitude, frequency, or intensity.

5. What are some real-life applications of waves and vibrations?

Waves and vibrations have numerous practical applications in everyday life. For example, sound waves are used in communication, while electromagnetic waves are used in wireless technology. Vibrations are also utilized in musical instruments, medical devices, and earthquake detection systems.

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