Question

Find the propagation velocity of a wave of wavelength 7.50 m . Find the period T for a wave of wavelength 7.50 m . On the East Coast of the United States, the National Weather Service frequently reports waves with a period of 3.92 s . Find the wavelength of these waves

Answer 1

velocity = 3.42 m/s

T = 2.19 s

wavelength = 0.4056 m

Step-by-step explanation:

given data

wavelength λ = 7.50 m

to find out

velocity , period T and wavelength when time 3.92 s

solution

we will apply first velocity formula that is

velocity =
`\sqrt{(wavelength*g)/(2\pi ) }` ..............1

put here all value g = 9.8, wavelength = 7.50

velocity =
`\sqrt{(7.50*9.8)/(2\pi ) }`

velocity = 3.42 m/s

and

time formula that is

velocity = wavelength × f ..............2

here f is frequency = 1/T .............3

so

velocity = wavelength × 1/T ..............4

T =
`(wavelength)/(velocity)`

T =
`(7.50)/(3.42)`

T = 2.19 s

and

wavelength by time 3.92

relation between wavelength and time is express as

T =
`\frac{wavelength}{\sqrt{(wavelength*g)/(2\pi ) } }` .............4

so

3.92 =
`\frac{wavelength}{\sqrt{(wavelength*9.8)/(2\pi ) } }`

3.92 =
`(wavelength)/(√(wavelength*1.5597))`

6.076 × wavelength = √wavelength

√wavelength = 1 / 6.076

wavelength = 0.4056 m