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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?
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.
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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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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? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about 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? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 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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