Wrong. A two-fold increase in CPU clock rate implies a twofold increase in CPU cycles per second, and nothing more. Any number of pure hardware improvements—for example, increasing the number of instructions, decreasing the number of CPU cycles an instruction takes to execute, improving I/O speed, etc—can improve performance without changing the clock rate, or even while decreasing the clock rate, without introducing parallel processing cores.
Wrong. A two-fold increase in CPU clock rate implies a twofold increase in CPU cycles per second, and nothing more. Any number of pure hardware improvements—for example, increasing the number of instructions, decreasing the number of CPU cycles an instruction takes to execute, improving I/O speed, etc—can improve performance without changing the clock rate, or even while decreasing the clock rate, without introducing parallel processing cores.