7. which has the shortest wavelength?\na 10 hz\nb 10 khz\nc 100 hz\nd 100 khz

Explanation:

Step1: Recall wave - speed formula

The wave - speed formula is $v = f\lambda$, where $v$ is the speed of the wave, $f$ is the frequency, and $\lambda$ is the wavelength. For electromagnetic waves in a vacuum, $v = c$ (speed of light, a constant). Rearranging for wavelength gives $\lambda=\frac{v}{f}$. When $v$ is constant, the wavelength $\lambda$ is inversely proportional to the frequency $f$. That is, the higher the frequency $f$, the shorter the wavelength $\lambda$.

Step2: Compare frequencies

We need to convert all frequencies to the same unit (Hz).

• Option a: $f_a = 10\ Hz$
• Option b: $10\ kHz=10\times10^{3}\ Hz = 10^{4}\ Hz$
• Option c: $f_c = 100\ Hz$
• Option d: $100\ kHz = 100\times10^{3}\ Hz=10^{5}\ Hz$

Since $10\ Hz<100\ Hz < 10^{4}\ Hz<10^{5}\ Hz$, the highest frequency is $100\ kHz$.

Answer:

d. 100 kHz