Answer:
<u>The options are: A, C and D</u>
Step-by-step explanation:
The sine wave has a general form : y = A sin (BX)
Where A is the amplitude and B = 2π/period
So, we will check which of the options will be a harmonic on a string that is 10 cm long.
A.) y=2sin(pi/5 x)
B = π/5 ⇒ period = 2π/B = 2π ÷ π/5 = 2π * 5/π = 10
So, one cycle of y=2sin(pi/5 x) will be a harmonic on a string that is 10 cm long.
B.) y=2sin(2pi/7 x)
B = 2π/7 ⇒ period = 2π/B = 2π ÷ 2π/7 = 7
C.) y=2sin(pi/10 x)
B = π/10 ⇒ period = 2π/B = 2π ÷ π/10 = 20 = 2 * 10
So, half a cycle of y=2sin(pi/10 x) will be a harmonic on a string that is 10 cm long.
D.) y=2sin(10pi x)
B = 10π ⇒ period = 2π/B = 2π ÷ 10π = 1/5 = 10/50
So, 50 cycles of y=2sin(10pi x) will be a harmonic on a string that is 10 cm long.
E.) y=2sin (5/2pi x)
B = 5/2π ⇒ period = 2π/B = 2π ÷ (5/2π) = 4π²/5
So, options <u>A, C and D</u> can be a harmonic on a string that is 10 cm long.
