Doppler Effect lab

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The College at Old Westbury *

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2700

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Chemistry

Date

Jan 9, 2024

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docx

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Department of Chemistry and Physics CP 2700-Wave Motion Exploratory Task Name Afrah Amer Part (I) Investigating the Doppler Effect https://www.compadre.org/osp/items/detail.cfm?ID=12399&Attached=1 Simulation Questions: 1. Click the play button to see a stationary source and receiver (Animation 1). Reset and use the pause and step buttons to verify that the period at the receiver (time elapsed from when one wave reaches the receiver until the next one reaches it) is 5.0 × 10 -3 s. What is the frequency of this wave? Answer: The time period between 2 successive waves has been verified to be 5.0 × 10 -3 s. The frequency of a wave is given by: f = T 1= 1 =200 Hz. 2. After there are several waves in the simulation pause it and use the mouse to find the wavelength (distance between two successive crests). What are the wavelength and speed of the wave (wavelength/period)? Answer: The distance between 2 successive crests is approximately equal to 1.72 m. Now, using the formula for frequency of a wave: Frequency of Wave = Wave Speed Wavelength f = v/λ v ⟹ = T/λ = 1.72 =344 m / s 5.0 × 10 −3 3. Now look at Animation 2, where the receiver is moving. Use the step button above to find the period (time between crests) as measured by the moving receiver when it is on the right of the source (moving towards the source). What is the frequency at the receiver if it is moving towards the source? Answer: In the case of receiver moving towards the source, the period is found out to be, T =4 × 10 −3 s. Similarly the frequency is calculated to be, f=1/T= 1 / 4.0 x 10 ^-3=250Hz.

4. When the receiver gets to the left of the source (moving away from the source) pause the simulation and measure the period. What is the frequency at the receiver if it is moving away from the source? Answer: In the case of receiver moving away from the source, the period is found out to be, T =7 × 10 −3 s Similarly, the frequency is calculated to be, f = 1/t = 1/7.0 × 10 −3. 5. Now look at Animation 3 which shows the source moving but the receiver stationary. Again, find the frequency while the source is on the left, moving towards the receiver, and the frequency when it is on the right moving away. Answer: the frequency when the source is on the left is calculated to be, f =1/T = 1/3.0 × 10 −3 =333.33 Hz the frequency when the source is on the right is calculated to be, f =1/T = 1/7.0 × 10 −3 =143 Hz Part (II) Using the Doppler Effect to Determine the Speed of a Moving Object Doppler Effect Formula for General Cases • The source and the observer could both be in motion; the observed frequency f 0 is given by the equation Where f s is the frequency of the source, v is the speed of the signal, v o is the speed of the object, and v s is the speed of the source. If either one is approaching we use positive values for v o and v s . If either one is moving away (receding) from the other we use negative values for v o and v s . For the case of the moving receiver and stationary source ( v s = 0) use the original frequency you found in question 1 ( f s ), the shifted frequency ( f o ) you found in question 3 and the speed of sound you found in question 2 ( v ) to find the speed of the observer ( v o ) Note that in this case, the equation becomes f o = fs

Answer: 250/ 200=344+ vo/ 34 ( 1.25∗344 ) −344= vo vo =86 m / s Reflections Discuss the sources of error in this experimental task, and how they affect your results. Answer: There are several sources of error in this experimental task that can affect the results: Human error in timing: When using the pause and step buttons to measure the period or time between crests, there could be slight variations in the timing due to human reaction time. Different individuals may have slightly different reaction times, which could introduce variability in the measured values. Inconsistent mouse measurements: When using the mouse to measure distances, such as the wavelength between crests, there is a potential for inconsistency in the measurements. Small variations in cursor placement or alignment could result in slightly different measurements each time, leading to altered results. Overall, these sources of error can affect the accuracy of the results obtained from the simulation. It is important to keep these sources of error in mind and attempt to minimize them as much as possible when conducting experiments or simulations.

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