To determine the missing wavelength value in brass when given the wave speed and frequency, we can use the relationship between wave speed, frequency, and wavelength. The formula that connects these quantities is:
[tex]\[ v = f \times \lambda \][/tex]
where:
- [tex]\( v \)[/tex] is the wave speed,
- [tex]\( f \)[/tex] is the frequency, and
- [tex]\( \lambda \)[/tex] is the wavelength.
Given values for brass:
- Wave speed [tex]\( v = 4700 \, \text{m/s} \)[/tex]
- Frequency [tex]\( f = 55 \, \text{Hz} \)[/tex]
We need to find the wavelength [tex]\( \lambda \)[/tex]. We can rearrange the formula to solve for wavelength:
[tex]\[ \lambda = \frac{v}{f} \][/tex]
Substitute the given values into the equation:
[tex]\[ \lambda = \frac{4700 \, \text{m/s}}{55 \, \text{Hz}} \][/tex]
Carrying out the division:
[tex]\[ \lambda \approx 85.45454545454545 \, \text{m} \][/tex]
Given the options:
A. 85
B. 98
C. 100
D. 112
The closest value to our calculated wavelength [tex]\( 85.45454545454545 \, \text{m} \)[/tex] is:
A. 85.
Thus, the missing wavelength value for brass is 85 meters.
