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For the wave y = 20 sin π (x/4 + t/2), the correct statement is (where x is in metre and time is in second)
- a)amplitude is 20 m and frequency is 0.25
- b)wavelength is 20 m and frequency is 1
- c)frequency is 1/2 and wavelength is 20 cm
- d)ω = 2π and K = π/2
Correct answer is option 'A'. Can you explain this answer?
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Most Upvoted Answer
For the wave y = 20 sin π (x/4 + t/2), the correct statement is (wher...
Explanation:
The given wave equation is y = 20 sin π (x/4 t/2). Let's analyze the different parameters of this equation.
Amplitude:
The amplitude of the wave is the maximum displacement from the equilibrium position. In this equation, the amplitude is 20 m as it is the coefficient of the sine function.
Frequency:
The frequency of the wave is the number of complete cycles per unit time. We can use the formula frequency = speed/wavelength. But in this equation, we can directly observe that frequency is 0.25 as the coefficient of 't' is 1/2. So, the wave completes 1 cycle in 4 seconds.
Wavelength:
The wavelength of the wave is the distance between two consecutive points in the same phase. We can use the formula wavelength = speed/frequency. But in this equation, we can observe that the coefficient of 'x' is 1/4. So, the wavelength is 4 times the value of 'x'. Therefore, wavelength = 20 m.
Angular frequency and wave number:
The angular frequency (ω) and wave number (K) are related to frequency and wavelength respectively. We can use the formulas ω = 2πf and K = 2π/λ. But in this equation, we can observe that frequency is 0.25 and wavelength is 20 m. Therefore, ω = 2π(0.25) = π/2 and K = 2π/20 = π/10.
Hence, the correct statement is option 'A' which says amplitude is 20 m and frequency is 0.25.
The given wave equation is y = 20 sin π (x/4 t/2). Let's analyze the different parameters of this equation.
Amplitude:
The amplitude of the wave is the maximum displacement from the equilibrium position. In this equation, the amplitude is 20 m as it is the coefficient of the sine function.
Frequency:
The frequency of the wave is the number of complete cycles per unit time. We can use the formula frequency = speed/wavelength. But in this equation, we can directly observe that frequency is 0.25 as the coefficient of 't' is 1/2. So, the wave completes 1 cycle in 4 seconds.
Wavelength:
The wavelength of the wave is the distance between two consecutive points in the same phase. We can use the formula wavelength = speed/frequency. But in this equation, we can observe that the coefficient of 'x' is 1/4. So, the wavelength is 4 times the value of 'x'. Therefore, wavelength = 20 m.
Angular frequency and wave number:
The angular frequency (ω) and wave number (K) are related to frequency and wavelength respectively. We can use the formulas ω = 2πf and K = 2π/λ. But in this equation, we can observe that frequency is 0.25 and wavelength is 20 m. Therefore, ω = 2π(0.25) = π/2 and K = 2π/20 = π/10.
Hence, the correct statement is option 'A' which says amplitude is 20 m and frequency is 0.25.
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Community Answer
For the wave y = 20 sin π (x/4 + t/2), the correct statement is (wher...
here amplitude =20 (from equation)
frequency= ANGULARVELOSITY/2 (PIE)
=PIE/2 /2PIE
= .25
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For the wave y = 20 sin π (x/4 + t/2), the correct statement is (where x is in metre and time is in second)a)amplitude is 20 m and frequency is 0.25b)wavelength is 20 m and frequency is 1c)frequency is 1/2 and wavelength is 20 cmd)ω = 2π and K = π/2Correct answer is option 'A'. Can you explain this answer?
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