The string at the right is 6.0 meters long and is vibrating as the third harmonic. The string vibrates up and down with 45 cycles in 10 seconds. Determine the frequency, period, wavelength, and speed for this wave

L = 6 m n = 3 f = 45/10 = 4.5 Hz → T = 1/f = 0.22 s

wavelength = 2L/n = 2×6÷3= 4 m

speed(v) = wavelength × f = 4×4.5 = 18 m/s

Explanation:

second solution for frequency:

f= speed(v) / wavelength = nv/2L = 3×18÷(2×6) = 4.5 Hz

the total distance that martina travels that day is

(distance from home to mom's office) plus (distance from mom's office to school)

plus (distance from school to library) plus (distance from library to friend's house)

plus (distance from friend's house to martina's house).

(we don't know what any of these distance actually is.)

find the surface area of the sphere to the nearest square unit. use a calculator.

a. 254 in.2

b. 64 in.2

c. 127 in.2

d. 1,018 in.2