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When we clap our hands, the sound produc...

When we clap our hands, the sound produced is best described by Here p denotes the change in pressure from the equilibrium value

A

`p = p_(0) sin (kx - omegat)`

B

`p = p_(0) sin kx cos omegat`

C

`p = p_(0) cos kx sin omegat`

D

`p = sump_(on) sin (k_(n)x - omega_(n)t)`

Text Solution

AI Generated Solution

The correct Answer is:
To solve the question regarding the sound produced when we clap our hands, we need to analyze the options provided and understand the nature of sound waves generated during the clap. ### Step-by-Step Solution: 1. **Understanding Sound Waves**: When we clap our hands, we create a disturbance in the air, which generates sound waves. These sound waves can be described mathematically. 2. **Analyzing the Options**: - **Option 1**: \( P = P_0 \sin(kx - \omega t) \) - This represents a simple harmonic wave traveling in one direction. - **Option 2**: \( P = P_0 \sin(kx) \cos(\omega t) \) - This represents a wave that can be seen as a product of two functions, indicating a stationary wave. - **Option 3**: \( P = P_0 \cos(kx - \omega t) \) - This is another form of a simple harmonic wave. - **Option 4**: \( P = \sum P_0 \sin(k_n x - \omega_n t) \) - This represents the summation of multiple waves, indicating the presence of a group of waves. 3. **Identifying the Correct Option**: - When we clap our hands, multiple sound waves of different frequencies and wavelengths are produced due to the rapid motion and the complex nature of the clap. Therefore, the sound produced is not just a single wave but a combination of many waves. - Hence, the best description of the sound produced when we clap our hands is given by **Option 4**, which accounts for the summation of multiple waves. ### Conclusion: The correct answer is **Option 4**: \( P = \sum P_0 \sin(k_n x - \omega_n t) \).
To solve the question regarding the sound produced when we clap our hands, we need to analyze the options provided and understand the nature of sound waves generated during the clap. ### Step-by-Step Solution: 1. **Understanding Sound Waves**: When we clap our hands, we create a disturbance in the air, which generates sound waves. These sound waves can be described mathematically. 2. **Analyzing the Options**: - **Option 1**: \( P = P_0 \sin(kx - \omega t) \) - This represents a simple harmonic wave traveling in one direction. ...
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Knowledge Check

  • An ideal gas enclosed in a cylindrical container supports a freely moving piston of mass M . The piston and the cylinder have equal cross-sectional area A . When the piston is in equilibrium, the volume of the gas is V_(0) and its pressure is P_(0) . The piston is slightly displaced from the equilibrium position and released. Assuming that the system is completely isolated from its surrounding, the piston executes a simple harmonic motion with frequency

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