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An ultrasound signal of frequency 50 KHz is sent vertically down into a medium. The signal gets reflected from a depth of 25 mm and returns to source 0.00005 seconds after it is emitted. The wavelength of the ultrasound signal in that medium is ________ cm.
Correct answer is between '1.99,2.01'. Can you explain this answer?
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An ultrasound signal of frequency 50 KHz is sent vertically down into ...
**Given Information:**
- Frequency of ultrasound signal (f) = 50 KHz = 50,000 Hz
- Depth of reflection (d) = 25 mm = 0.025 m
- Time taken for signal to return (t) = 0.00005 s
**Formula:**
The speed of ultrasound in a medium is given by the equation:
v = λf
where v is the velocity of ultrasound, λ is the wavelength of ultrasound, and f is the frequency of ultrasound.
**Solution:**
1. Calculate the velocity of ultrasound in the medium using the formula:
v = d/t
v = 0.025 m / 0.00005 s
v = 500 m/s
2. Substitute the value of velocity (v) and frequency (f) into the equation v = λf to find the wavelength (λ):
500 = λ * 50,000
λ = 500 / 50,000
λ = 0.01 m
3. Convert the wavelength from meters to centimeters:
λ (cm) = λ (m) * 100
λ (cm) = 0.01 m * 100
λ (cm) = 1 cm
Therefore, the wavelength of the ultrasound signal in the medium is 1 cm.
Since the correct answer is given as between 1.99 and 2.01 cm, there may be a mistake in the calculation or the given information. Please double-check the values and calculations to ensure accuracy.
- Frequency of ultrasound signal (f) = 50 KHz = 50,000 Hz
- Depth of reflection (d) = 25 mm = 0.025 m
- Time taken for signal to return (t) = 0.00005 s
**Formula:**
The speed of ultrasound in a medium is given by the equation:
v = λf
where v is the velocity of ultrasound, λ is the wavelength of ultrasound, and f is the frequency of ultrasound.
**Solution:**
1. Calculate the velocity of ultrasound in the medium using the formula:
v = d/t
v = 0.025 m / 0.00005 s
v = 500 m/s
2. Substitute the value of velocity (v) and frequency (f) into the equation v = λf to find the wavelength (λ):
500 = λ * 50,000
λ = 500 / 50,000
λ = 0.01 m
3. Convert the wavelength from meters to centimeters:
λ (cm) = λ (m) * 100
λ (cm) = 0.01 m * 100
λ (cm) = 1 cm
Therefore, the wavelength of the ultrasound signal in the medium is 1 cm.
Since the correct answer is given as between 1.99 and 2.01 cm, there may be a mistake in the calculation or the given information. Please double-check the values and calculations to ensure accuracy.
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An ultrasound signal of frequency 50 KHz is sent vertically down into a medium. The signal gets reflected from a depth of 25 mm and returns to source 0.00005 seconds after it is emitted. The wavelength of the ultrasound signal in that medium is ________ cm.Correct answer is between '1.99,2.01'. Can you explain this answer?
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An ultrasound signal of frequency 50 KHz is sent vertically down into a medium. The signal gets reflected from a depth of 25 mm and returns to source 0.00005 seconds after it is emitted. The wavelength of the ultrasound signal in that medium is ________ cm.Correct answer is between '1.99,2.01'. Can you explain this answer? for IIT JAM 2024 is part of IIT JAM preparation. The Question and answers have been prepared according to the IIT JAM exam syllabus. Information about An ultrasound signal of frequency 50 KHz is sent vertically down into a medium. The signal gets reflected from a depth of 25 mm and returns to source 0.00005 seconds after it is emitted. The wavelength of the ultrasound signal in that medium is ________ cm.Correct answer is between '1.99,2.01'. Can you explain this answer? covers all topics & solutions for IIT JAM 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for An ultrasound signal of frequency 50 KHz is sent vertically down into a medium. The signal gets reflected from a depth of 25 mm and returns to source 0.00005 seconds after it is emitted. The wavelength of the ultrasound signal in that medium is ________ cm.Correct answer is between '1.99,2.01'. Can you explain this answer?.
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